If you are going fly fishing, you need to have your critical gear with you while wading and casting. One of the critical pieces of equipment is your vest.
Fly Fishing Accessories – Hanging Stuff Around Your Chest
Construction workers have tool belts to hold everything they need while working. Fly fishing anglers have the same thing in the vest. They hold your tools of the fly fishing trade. Without them, you will be endlessly hunting for flies, repellant, grapplers and so on.

This necessary fly fishing clothing comes in a variety of styles. Old school vests are the best in my opinion. They fit and look like regular clothing vests, but are made with mesh pockets and water proofing material. I find they are perfect for holding the necessary fly fishing gear. They are also good because the distribute the weight of your junk…err, gear across your shoulders and back.

Any fly fishing gear shop should have them.
Being a consumer society, more than a few companies have come up with advancements in ways to carry around your gear. Typically, they come in the form of modular systems hanging over the shoulder. They look like travel fannypacks hanging off the front of each shoulder. Depending on the brand, they may have a rear or front fanny pack and even both. Some anglers love these more modern gear accessories. Personally, I find them ungainly and annoying, but to each their own. I strongly suggest you fit yourself with one of these new systems before committing to buy them.
When considering how you will hold your stuff, you should give a good bit of thought to what you want it to hold. Personally, I want mine to hold sunscreen for my bald head, insect repellent, clippers, forceps, a poncho for rain, my car keys, line and, of course, flies.

I don’t like hauling my stuff up and down the shore, so I tend to load up like a Sherpa. You might prefer a less demanding approach. The point is to figure out what is best for you and then buy a version that meets your needs.
If you are going to get serious about angling, you will need to a way to lug your stuff around with you. Figure out what you want to put in yours and then make your selection.